Thank you both for your responses and help. I figured out what is wrong with my setup this morning. The issue was the "Exclude from application evaluation" option was not checked for the point generate ID attribute rules. I tried using just the sequence name in the NextSequenceValue, but that still generated the same error message. While looking through the help documentation I found a note about the "Exclude from application evaluation" setting must be checked when working with sequences.
https://pro.arcgis.com/en/pro-app/latest/help/data/geodatabases/overview/evaluate-attribute-rules.ht...
So I checked that setting and I could add new addresses again. The odd thing is I looked at the 2.6 version of the help documentation and it has a similar note. That is odd to me because I have been using this solution since July with that setting unchecked and it has been working just fine. I guess that was a bug in 2.6 that allowed those rules to execute.
@ChrisFox I just want to let you know that I unzipped the Address Management Solution that I downloaded back in July and the default generate ID attribute rules for all the point layers have the "Exclude from application evaluation" unchecked. The road generate ID attribute rule does have the setting checked.
@JoeBorgione I found out that 2.7 does not care if the name is "AddressPointID" or "db.name.AddressPointID". Either format will work. I was sure I had to use "db.name.AddressPointID" in 2.6 to get the rule to work but I may be misremembering.
"Not all those who wander are lost" ~ Tolkien